Just like how regular velocity had units of meters per second,Īngular velocity has units of radians per second. Since delta theta, theĪngular displacement is in radians, and the time is in seconds. And the units of omega, angular velocity, are going to be radians per seconds. Which looks like a w, but it's really the Greek letter omega. Represent angular velocity is the Greek letter omega, Going to be the angular displacement per time. If regular velocity isĭisplacement per time, the angular velocity is So down here we'll defineĪ similar quantity, but it's going to be the angular velocity, which is defined analogously Quantities that was called the velocity of theīall, and it was defined to be the displacement per time. Just like up here, knowingĪbout the displacement is good, but you might want to know about the rate that it's being displaced. Has rotated through, but another quantity that might be useful is the rate at which it's To quantify the amount of angle that this ball And that's just usuallyĬalled the displacement, which is measured in meters. Regular displacement was a defined b, the final position minus the initial positions, Regular displacement, so if you imagine a tennis ball just going in a straight line, the That this is analogous to how we defined the Reasons that I'll show you in just a second. The angular displacement and we typically measure it in radians, as opposed to degrees for In which case the angular displacement would be 90ĭegrees or pi over two radians. Our theta initial couldīe over here at 180, and we'd go down to 270, Two whole revolutions, which would be either 720ĭegrees or four pi radians. Way, and then another circle all the way, our angularĭisplacement wouldn't be zero. And if we started at zero and went through an entire circle all the So our angular displacement would be 180 degrees or pi radians. Theta final would be 180, theta initial would be zero, Tennis ball over here at zero and we ended it at 180, And it's given the symbol delta theta, because theta is the angleĪnd delta theta is the change in the angle, so this is really theta final minus theta initial. We could define a quantity that just says how much angle Tennis ball starting there and it rotates over to here, Just be how much angle has this tennis ball swung The most basic quantity you'd come up with would Wanted to start defining motion variables that wouldĭescribe the rotational motion of this tennis ball, maybe You tie a string to it, and you whirl the tennisīall around in a circle. Mean, how they're defined, and how you can solve for Go over all the different rotational variables likeĪngular displacement, angular velocity, andĪngular exhilaration. That for many people the hardest part about solvingĪ rotational motion problem is just keeping track of all the new names for all the rotational

For that you need to understand commutative vector law. NOTE: A rigorous mathematical answer can be given regarding why angular displacement is not like linear vector displacement. This is where the properties of vectors come forth.Īlthough defined in a similar fashion like displacement, that is, as the difference between the final (angular) position - initial (angular) position, angular displacement is not a vector. However, you can argue that we can define something like shortest angular path for angular motions, analogous to linear displacement. An arc between any two point is always greater than a line between them. In circular motions you move in arcs not straight lines and the concept of shortest distance as defined in angles, is moot. When you talk about shortest path between two position coordinates in space, you, in principle, invoke vector laws to find the change in the position vectors which in turn tells you the displacement or the shortest distance you traveled from one position coordinate to the other. Angular displacement unlike linear displacement isn't defined as the shortest path traveled between to points. Since you did not ask why angular displacement is not a vector, let me give a simpler answer to what you asked, without going into commutative vector laws.

Omega in physics